SUM OF THREE CUBES

[Timothy Y. Chow]

Harvey Friedman wrote:
> QUESTION: Is the set of all sums of three cubes of integers recursive? 
> It is obviously recursively enumerable.
>
> This seems to be the most attractive set of integers for which it is not 
> known whether it is recursive. Any competitors?

Oh, here's another candidate that I forgot to mention in my previous 
message: the set of all integers that appear exactly 6 times in Pascal's 
triangle.

https://en.wikipedia.org/wiki/Singmaster%27s_conjecture

The set is known to be infinite, but I don't think that it is even known 
to be recursively enumerable.

Tim